Term 2 week 3 Choice Under uncertainty further topics Flashcards
What is the relation between asymetric information and insurance?
In insurance markets the individual has more information about themself than the insurance company has about the individual
How do you find the optimal level of insurance?
What is the reasoning behind why this can work?
You write the expected utility function taking into account the good and the bad state then take the derivative with respect to K
With actuarily fair insurance and risk averse how much do you buy?
You insure yourself for the difference between the good and the bad state
What is the issue between imperfect information and insurance markets?
What is the solution to this?
Insurance company cannot identify careful household from careless household.
Careless household prefers the insurance of careful household as the premium is lower.
A self-separating equilbirium
What is a self-separating equilibrium?
How is it done?
One which makes the careful and non-careful choose the bundle that is made for them.
Done by making the careless household optimise but make the careful household be on a point to the left of the careless whilst on careful budget constraint.
What is screening and how can it be introduced to the self-separating equilibrium
Insurance firm pays a fixed cost F to screen people and get data.
This then gets passed onto the household as an extra cost plus the insurance premium.
This separates the equilibrium
What is state dependent utility and how is this added to the choices under uncertainty model
State dependent utility means utility in good and bad state is different
a transformation sigma is put on utility in the good state where sigma is between 1 and 0
Where sigma is a trauma factor between 0 and 1 with 1 being no trauma
How do you show that in state dependent utility (actuarily fair) people do not buy full insurance?
Start off with expected utility
(1-p)u(wg - gammak) +psigma . u(wb +(1-gamma)K) = U(wg,wb)
Then take derivative W.R.T K
-gamma(1-p) . u’(wg -gammak) + (1-gamma)psigmau’(wb + (1-gamma)K) = 0
then = row to gamma as it is actuarily fair
so u’((wg -gammak) = sigmau’(wb +(1-p)k)
as sigma is between 0 and 1
u’(wg-pk) < u’(wb+K(1-p)
as utility function has unique input for output
wg - pk < wb+K(1-p)
K< wg - wb
For all types of utility function with a trauma factor they will not buy full insurance.
What is the intuition behind not buying full insurance in state dependent utility?
As the MU of wealth in bad state is lower
Do an optimal insurance for actuarily fair with a log function
How do we show how it depends on sigma
What is required for insurance?
sigma > wb/wg
What is the relationship between trauma and insurance?
You will have more insurance when trauma is less.
What is important about the power utility function?
What is pi in this?
How do you find how risk aversion impacts
As pi gets closer to 1 it converges to a logarithmic function
pi is the coefficent of relative risk aversion
How do you draw a utility function under insurance?
You fix an expected utility function for a particular level of utility U bar
then you solve it for wg
Graphically how does state dependent utility curve and non-state dependent utility curve look like
X axis is wbad state
Y axis is wgood state
Indifference curve for non-state dependent is steeper
Indifference curve for state dependent is state shallower
This is because the state-dependent has low mu in bad state so willing to trade away bad state for small numbers of good state.
What is the model setup for portfolio analysis
What is the expected utility
What can the derivative of expected utility show
Individual has wealth w
wants to invest x
two states good wg and wb
two rates of return rg and rb
wg = w -x + x(1+rg) = w+xrg
wb = w - x +x(1+rb) = w+ xrb
U(x) = (1-p)u(w+xrg) + pu(w+xrb)
